The ratio of pennies to dimes I have is 3:5. I have a 2:3 ratio of dimes to quarters. If I have 75 quarters, how many pennies do I have?
If you have 75 quarters, at ratio of 2:3, you must have 50 dimes.
Thus, with 50 dimes and ratio of 3:5, you must have 30 pennies.
Well, if you have a 2:3 ratio of dimes to quarters and you have 75 quarters, then according to the ratio, you would have (2/3) * 75 = 50 dimes.
Now, since the ratio between pennies and dimes is 3:5, let's calculate the number of pennies.
We know the ratio is 3:5, so for every 5 dimes, there are 3 pennies.
Therefore, for 50 dimes, we would have (3/5) * 50 = 30 pennies.
So, you would have 30 pennies. Just be careful with them; they can be quite the pranksters!
To solve this, let's break it down step by step:
Step 1: Determine the number of dimes
Since the ratio of pennies to dimes is 3:5, it means that for every 3 pennies, there are 5 dimes. Let's represent the number of dimes with the variable "d". To find the number of dimes, we can set up the following proportion:
3 pennies / 5 dimes = x pennies / 75 dimes
Cross multiplying, we get:
3 * 75 = 5 * x
225 = 5x
So, x = 225 / 5
x = 45
Therefore, you have 45 dimes.
Step 2: Determine the number of quarters
From the given information, the ratio of dimes to quarters is 2:3. This means that for every 2 dimes, there are 3 quarters. Let's represent the number of quarters with the variable "q". Setting up the proportion:
2 dimes / 3 quarters = 45 dimes / x quarters
Cross multiplying, we get:
2 * x = 3 * 45
2x = 135
So, x = 135 / 2
x = 67.5
Since we cannot have half a quarter, we round down to the nearest whole number.
Therefore, you have 67 quarters.
Step 3: Determine the number of pennies
Now that we know the number of quarters (67) and the ratio of pennies to dimes (3:5), we can find the number of pennies.
For every 3 pennies, there are 5 dimes. Since we have 45 dimes, we can set up the following proportion:
3 pennies / 5 dimes = x pennies / 45 dimes
Cross multiplying, we get:
3 * 45 = 5 * x
135 = 5x
So, x = 135 / 5
x = 27
Therefore, you have 27 pennies.
In conclusion, you have 27 pennies
To find the number of pennies you have, we can follow a step-by-step process:
Step 1: Determine the number of dimes.
Given that you have a 2:3 ratio of dimes to quarters, and you have 75 quarters, we can calculate the number of dimes using the proportion:
2/3 = x/75
Cross-multiplying, we get:
3x = 2 * 75
3x = 150
Dividing both sides by 3, we find:
x = 50
So, you have 50 dimes.
Step 2: Determine the number of pennies.
Now that we know the number of dimes, we can use the ratio of 3:5 to find the number of pennies. Given that the ratio of pennies to dimes is 3:5, we can set up the following proportion:
3/5 = p/50
Cross-multiplying gives:
5p = 3 * 50
5p = 150
Dividing both sides by 5, we find:
p = 30
Therefore, you have 30 pennies.